Doing in SAS Enterprise softwareAs an independent statistical consultant, you have been contracted...

Question

Doing in SAS Enterprise softwareAs an independent statistical consultant, you have been contracted by Henry Oldman, a collector of grandfather clocks. Mr Oldman has observed auction sales of 32 grandfather clocks, collecting data on: · The selling price (Price) · The age of the clock (Age) · The number of bidders on the clock (Bidders) · The quality of the clock (Quality: 1=good, 0=normal) Mr Oldman is interested in selling three clocks from his collection: 	Clock name 	Age (years) 	Expected bidders 	Quality 	Masterton 	130 	5 	Good 	Palmerston 	140 	8 	Normal 	Halverson 	175 	10 	Good He would like you to predict the selling price of each clock, and also to tell him whether you believe he should spend $200 to restore the Palmerston's clock condition from Normal to Good. Tasks: Require doing in SAS Enterprise  1. Create box-and-whisker and scatter plots (as appropriate) to show how each of the x-variables affects the price of the clocks.  2. Create a multiple regression model for price using all three x-variables. 3. Interpret the parameter estimates. 4. Predict the price of each of Mr Oldman's three clocks. Provide the most likely selling price, along with a 95% prediction interval. Tell Mr Oldman how to interpret the 95% prediction interval. 5. Decide (using your model) whether spending $200 to upgrade the Palmerston clock from Normal to Good quality is worthwhile (i.e. can be expected to earn more than $200 back at auction). 6. Write your findings in a case report, and upload it below by Sunday night.

Pooja · Accepted Answer

Introduction
The variable to be predicted is the selling price of the clock. The variable on the basis of which predictions are made is age of the clock, expected bidders, and quality of the clock. I want to build a multiple regression model that can predict the selling price of Clock on the basis of its age, bidders, and quality.
Data
The variables which are measured by the ratio scale of measurement are the selling price of the clock, age of the clock, and expected bidders on the clock. The variable which is measured by the nominal scale of measurement is the quality of the clock. The quality of the clock is categorised as either good or normal. The good quality clock is coded as 1 and the normal quality clock is coded as 0.
Analysis
The dependent variable is the selling price which is plotted on the y-axis. The independent variables are the age of the clock, the number of Bidders on the clock and the quality of the clock. The independent variables are plotted on the x-axis in the scatter plot. The three-scatter plot is given below.
 
There is a strong positive linear relationship between the age of the clock and its selling price. An upward trend with all points close to each other is an indication for the same. With an increase in the age of the clock, the selling price increases drastically
There is a moderate positive linear relationship between the number of bidders on the clock and its selling price. An upward trend with all points moderately close to each other is an indication for the same. With an increase in the bidders on the clock, the selling price also increases.
The box plot for price bidders and age is given below. The box plot is plotted for the variables which are measured by the ratio scale of measurement.
There are no significant outliers in the data set. The middle line of the box in the box plot indicates that the distribution for all the three variables is approximately normal.
The multiple Regression model is given by:  selling price = -1284.2193 + 12.6208*age + 85.7962*bidders + 124.0003*quality
	Regression Analysis
	
	
	Regression Statistics
	Multiple R
	0.9537
	R Square
	0.9095
	Adjusted R Square
	0.8998
	Standard Error
	126.8486
	Observations
	32
	ANOVA
	
	
	
	
	
	 
	df
	SS
	MS
	F
	Significance F
	Regression
	3
	4529864.1646
	1509954.7215
	93.8410
	0.0000
	Residual
	28
	450535.8354
	16090.5656
	
	
	Total
	31
	4980400.0000
	 
	 
	 
	 
	Coefficients
	Standard Error
	t Stat
	P-value
	Lower 95%
	Upper 95%
	Intercept
	-1284.2193
	165.2268
	-7.7725
	0.0000
	-1622.6710
	-945.7676
	Age
	12.6208
	0.8684
	14.5336
	0.0000
	10.8420
	14.3996
	Bidders
	85.7962
	8.3032
	10.3329
	0.0000
	68.7878
	102.8046
	Quality
	124.0003
	45.6578
	2.7159
	0.0112
	30.4745
	217.5261
With 1 year an increase in age of the clock, the price of the clock is increased by $12.6208.

As an independent statistical consultant, you have been contracted by Henry Oldman, a collector of grandfather clocks. Mr Oldman has observed auction sales of 32 grandfather clocks, collecting data...

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